Any that you cannot buy easily in a (UK) store will have a link to an online supplier next to it.
Brands whose brushes are all Vegan:
Beauty Without Cruelty http://www.bwcshop.com/accessories-2/
Furless http://furlesscosmetics.com.au/ (not UK but shipping is pretty quick and reasonable)
Neve http://www.cocktailcosmetics.co.uk/cat/brushes/neve-cosmetics or http://www.nevecosmetics.it/
Hope this is useful! This list is by no means exhaustive, so if I've missed your fave brand, leave me a comment and I'll add them.
If you want to see that video, I will link it below when it's up :)
Last updated: 10 August 2017